Which of the following numbers is a factor of 188? ${2,5,9,10,11}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $188$ by each of our answer choices. $188 \div 2 = 94$ $188 \div 5 = 37\text{ R }3$ $188 \div 9 = 20\text{ R }8$ $188 \div 10 = 18\text{ R }8$ $188 \div 11 = 17\text{ R }1$ The only answer choice that divides into $188$ with no remainder is $2$ $ 94$ $2$ $188$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $188$ $188 = 2\times2\times47 2 = 2$ Therefore the only factor of $188$ out of our choices is $2$. We can say that $188$ is divisible by $2$.